Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x+y &= -2 \\ -8x+3y &= -6\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $3y = 8x-6$ Divide both sides by $3$ to isolate $y$ $y = {\dfrac{8}{3}x - 2}$ Substitute this expression for $y$ in the first equation. $-x+({\dfrac{8}{3}x - 2}) = -2$ $-x + \dfrac{8}{3}x - 2 = -2$ Simplify by combining terms, then solve for $x$ $\dfrac{5}{3}x - 2 = -2$ $\dfrac{5}{3}x = 0$ $x = 0$ Substitute $0$ for $x$ back into the top equation. $- 0+y = -2$ $y = -2$ $y = -2$ $y = -2$ The solution is $\enspace x = 0, \enspace y = -2$.